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A functional version of the LaSalle invariance principle is introduced. Rather than the usual pointwise Lyapunov-like functions, this extended version of the principle uses specially constructed functionals along system trajectories. This modification enables the original principle to handle not only autonomous, but also some nonautonomous systems. The new theoretical result is used to study robust synchronization of general Liénard-type nonlinear systems. The new technique is finally applied to coupled chaotic van der Pol oscillators to achieve synchronization. Numerical simulation is included to demonstrate the effectiveness of the proposed methodology.
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Chen et al. (2009) studied this question.
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